Clefs are the strange little symbols at the beginning of each staff. They provide information such as which instrument might be playing, what range of notes is being used, and how to read the staff. This means that depending on which one you are using, the lines of the staff will be different. For instance in the Treble, the bottom line of the staff is E, while in the Bass, the bottom line of the staff is G. If you start playing the wrong notes because you misread or forgot one of these, it could be very confusing and sound VERY bad.
We will begin with the treble since it is the most common.
This is read by instruments such as the guitar, violin, piccolo, some viola playing, and certain (usually female) voices. Basically, it is usually played by the higher pitched instruments. The lines from top to bottom are E G B D F. You can memorize this by saying "Every Good Boy Does Fine." It's lame, I know, but it has worked for school children for decades upon decades so there must be something to it. The spaces spell out the word FACE. When we play notes above or below the staff, we use what we call ledger lines. These are short lines we use as an extension of the range of the staff. To find these notes, just count down or up, always alternating between line and space.
This is sometimes called the G clef because the loop of it wraps around the second line from the bottom which is a G note in this one. (Some say it's because it kind of looks like a cursive letter G, but I don't really buy that.)
This is played by such instruments as the tuba, electric and acoustic basses, the left hand on a piano, etc. Bassically (pun fully intended) it is played by the lower pitched instruments. The lines on it are G B D F A. You can remember this one by saying "Good Boys Do Fine Always". The spaces are A C E G. This doesn't spell a work, but you can remember it by saying "All Cows Eat Grass". Ledger lines work the same way here.
This is sometimes called the F clef because the two dots on it are on either side of the 4th line from the bottom, which in this one is an F note.
There are other ones out there, such as the Alto and the Tenor , but we will cover them later. They are harder to memorize and are only used by certain instruments so they are not seen that often.
Sometimes a piece of music will switch from one to another. The viola is usually read in alto. But for higher passages, rather than using ledger lines forever, sometimes the music will switch to Treble, just to make it easier to read.
Memorize these two and become fluent in them. Even if you only plan on using the treble (say you're a violinist) you should learn the bass because the bass lines are usually what determine the chord progressions in a song. Even if you are a bass player, you should learn the treble because most music is written in it, and it will be necessary in learning certain music. For that reason, treble is what we will mainly use for the majority of these lessons. Learning others can be useful, but be SURE you learn at least these two.
That's pretty much all there is to these. They are necessary because they inform the staff. With out one of these things at the beginning of each line, we wouldn't know what the lines meant. As you can see from the explanation above, the lines mean different things in treble and bass. Later there will be even more differences when we enter the world of Alto and Tenor, and so on. So go ahead and get used to using at least these two. (The others aren't as necessary if you don't play those instruments.)
Hope this helps! Practice hard and let me know if you have any questions!